Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow

• Author(s): Esua John Maxwell; Ehigiator Emihia Lucky; Ekundayo Oluwatobi Favour; Olalekan Rafiat Olatomiwa; Dr. Adeola Grace Olugbengba
• Paper ID: 1719694
• Page: 1632-1643
• Published Date: 18-07-2026
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 10 Issue 1 July-2026

Abstract

The flow of fluids through pipes is a fundamental problem in engineering, governing the performance of systems ranging from water distribution networks to chemical reactors. This work presents a comprehensive analysis of internal pipe flow using the Navier–Stokes equations as the foundational framework. Under assumptions of steady, incompressible, Newtonian, and fully developed flow, the governing equations are simplified and solved analytically for laminar conditions, yielding the classical parabolic velocity profile, the Hagen–Poiseuille solution. The derivation is complemented by dimensional analysis, which reveals the universal nature of the laminar velocity distribution when expressed in dimensionless form. Numerical validation using realistic fluid properties confirms the theoretical predictions and illustrates the sensitivity of flow rate to pipe radius. A comparison with turbulent flow regimes highlights the transition in momentum-transport mechanisms as Reynolds number increases, with turbulent profiles described by empirical correlations such as the one-seventh power law and the logarithmic law of the wall. The results provide not only a rigorous theoretical foundation but also practical insights for the design and optimization of piping systems in engineering applications.

Keywords

Hagen–Poiseuille Flow, Laminar Flow, Momentum Transport, Navier–Stokes Equations, Pipe Flow, Reynolds Number, Turbulent Flow.

Citations

IRE Journals:
Esua John Maxwell, Ehigiator Emihia Lucky, Ekundayo Oluwatobi Favour, Olalekan Rafiat Olatomiwa, Dr. Adeola Grace Olugbengba "Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow" Iconic Research And Engineering Journals Volume 10 Issue 1 2026 Page 1632-1643

IEEE:
Esua John Maxwell, Ehigiator Emihia Lucky, Ekundayo Oluwatobi Favour, Olalekan Rafiat Olatomiwa, Dr. Adeola Grace Olugbengba "Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow" Iconic Research And Engineering Journals, vol. 10, no. 1, Jul. 2026

APA:
Esua John Maxwell, Ehigiator Emihia Lucky, Ekundayo Oluwatobi Favour, Olalekan Rafiat Olatomiwa, Dr. Adeola Grace Olugbengba (2026). Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow. Iconic Research And Engineering Journals, 10(1).

MLA:
Esua John Maxwell, Ehigiator Emihia Lucky, Ekundayo Oluwatobi Favour, Olalekan Rafiat Olatomiwa, Dr. Adeola Grace Olugbengba "Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow" Iconic Research And Engineering Journals, vol. 10, no. 1, Jul. 2026.

BibTeX

@article{1719694,
author = {Esua John Maxwell, Ehigiator Emihia Lucky, Ekundayo Oluwatobi Favour, Olalekan Rafiat Olatomiwa, Dr. Adeola Grace Olugbengba},
title = {Navier–Stokes Equation (NSE) in the Transport Phenomena for Momentum Transport in Pipe Flow},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {1},
pages = {1632-1643},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1719694.pdf},
abstract = {The flow of fluids through pipes is a fundamental problem in engineering, governing the performance of systems ranging from water distribution networks to chemical reactors. This work presents a comprehensive analysis of internal pipe flow using the Navier–Stokes equations as the foundational framework. Under assumptions of steady, incompressible, Newtonian, and fully developed flow, the governing equations are simplified and solved analytically for laminar conditions, yielding the classical parabolic velocity profile, the Hagen–Poiseuille solution. The derivation is complemented by dimensional analysis, which reveals the universal nature of the laminar velocity distribution when expressed in dimensionless form. Numerical validation using realistic fluid properties confirms the theoretical predictions and illustrates the sensitivity of flow rate to pipe radius. A comparison with turbulent flow regimes highlights the transition in momentum-transport mechanisms as Reynolds number increases, with turbulent profiles described by empirical correlations such as the one-seventh power law and the logarithmic law of the wall. The results provide not only a rigorous theoretical foundation but also practical insights for the design and optimization of piping systems in engineering applications.},
keywords = {Hagen–Poiseuille Flow, Laminar Flow, Momentum Transport, Navier–Stokes Equations, Pipe Flow, Reynolds Number, Turbulent Flow.},
month = {July}
}